Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Electronic structure and optical gain of truncated InAs1-xNx/GaAs quantum dots

The shape of truncated square-based pyramid quantum dots (QDs) is similar to that of real QDs in experiments. The electronic band structures and optical gain of InAs1-xNx/GaAs QDs are calculated by using the 10-band k.p model, and the strain is calculated by the valence force field (VFF) method. When the top part of the QD is truncated, greater truncation corresponds to a flatter shape of the QD. The truncation changes the strain distribution and the confinement in the z direction. A flatter QD has a greater C1-HH1 transition energy, greater transition matrix element, less detrimental effect of higher excited transition, and higher saturation gain and differential gain. The trade-off between these properties must be considered. From our results, a truncated QD with half of its top part removed has better overall performance. This can provide guidance to growing QDs in experiments in which the proper growing conditions can be controlled to achieve required properties. (C) 2009 Elsevier Ltd. All rights reserved.

Four-dimensional Newton's constant in brane world with a sloping extra dimension

We show the four-dimensional Newton's constant obtained naturally from five-dimensional brane world with a tinily sloping extra dimension, which is independent of the bulk Weyl tensor. The corresponding universe is stiff fluid dominated when the slope of extra dimension is very small. Otherwise, the universe may be undergoing a self-acceleration at present epoch and have a decelerated phase in very recent past.

Purification and characterization of recombinant truncated human interleukin-11 expressed as fusion protein in Escherichia coli

Mature human interleukin-11 (HuIL-11) is a cytokine consisting of 178 amino acid residues that results from scission of the N-terminal signal peptide, consisting of 21 amino acid residaues, from the corresponding nascent polypeptide. A DNA fragment encoding a truncated HuIL-11 (trHuIL-11), with an additional 5 amino acid residues removed from the N-terminus, was cloned into vector pGEX-2T between the BamHI site and the EcoRI site. Upon transformation with Escherichia coli BL21, the construct over-produced a glutathione S-transferase (GST)-fused protein in a soluble form after IPTG induction. The fusion protein was initially fractionated with butyl-Sepharose 4 fast flow column and by affinity chromatography using a GSH-Sepharose 4B column. On-site enzymatic release with thrombin gave the target protein at 96% purity as judged by SDS-PAGE and HPLC. Expression of the interleukin as a GST-fused protein thus greatly improved downstream processing. Subsequent biological activity assay suggested that trHuIL-11 had similar activity profile to the naturally produced sample and may be a promising candidate for further development as biopharmaceutical.

喷涂于运动固壁上的模口流变流动

模口膨胀是聚合物加工中的重要现象，通常用流变效应来解释． 射流自由面上温度分布不均匀，必然会产生表面张力梯度驱动的热毛细对流．采用二维非定常有限元方法，数值模拟喷涂于运动固壁上的流变流体的模口膨胀问题．计算中考虑了流变效应和热毛细效应的耦合作用．结果表明，流变效应和热毛细效应两者均使射流截面增大，非Newton流体的流变效应是模口膨胀的主要原因．

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

Energy Conversion in Shape Memory Alloy Heat Engine Part I: Theory

Shape Memory Alloy (SMA) can be easily deformed to a new shape by applying a small external load at low temperature, and then recovers its original configuration upon heating. This unique shape memory phenomenon has inspired many novel designs. SMA based heat engine is one among them. SMA heat engine is an environment-friendly alternative to extract mechanical energy from low-grade energies, for instance, warm wastewater, geothermal energy, solar thermal energy, etc. The aim of this paper is to present an applicable theoretical model for simulation of SMA-based heat engines. First, a micro-mechanical constitutive model is derived for SMAs. The volume fractions of austenite and martensite variants are chosen as internal variables to describe the evolution of microstructure in SMA upon phase transition. Subsequently, the energy equation is derived based on the first thermodynamic law and the previous SMA model. From Fourier’s law of heat conduction and Newton’s law of cooling, both differential and integral forms of energy conversion equation are obtained.

喷涂于运动边界上液体薄膜射流的流变效应

采用非Newton流体的二阶流体模型分析了相对高温的液体熔体薄膜由模口喷出并涂于运动的固体膜上，讨论了由自由面上温度梯度驱动的非Nweton液体薄膜的热毛细流动，考虑热毛细流动的流变效应，分析是工于润滑理论近似和摄动理论近似，得到了液体高度方程和非Newton液体薄膜的热流体力学过程描述，具体求解了弱流变流体效应的情况。

The Capillary Force In Micro- And Nano-Indentation With Different Indenter Shapes

The influence of the indenter shapes and various parameters on the magnitude of the capillary force is studied on the basis of models describing the wet adhesion of indenters and substrates joined by liquid bridges. In the former, we consider several shapes, such as conical, spherical and truncated conical one with a spherical end. In the latter, the effects of the contact angle, the radius of the wetting circle, the volume of the liquid bridge, the environmental humidity, the gap between the indenter and the substrate, the conical angle, the radius of the spherical indenter, the opening angle of the spherical end in the truncated conical indenter are included. The meniscus of the bridge is described using a circular approximation, which is reasonable under some conditions. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. The results can be applicable to the micro- and nano-indentation experiments. It shows that the measured hardness is underestimated due to the effect of the capillary force. (c) 2008 Elsevier Ltd. All rights reserved.

Rheological flow from a die and painting on a moving solid wall

Die swell is an important, phenomenon. in polymer processing, and is explained usually by rheological properties of the fluid. Because of the nonuniform of temperature distribution on the free surface of the liquid jet, the thermo capillary convection driven by surface tension gradient exists. The rheological fluid flowing out of a die and painting on a moving solid wall is studied by the numerical finite element method of a two-dimensional and unsteady model in the present paper, and both the rheological effect of a non-Newtonian fluid and the thermocapillary effect are considered. The results show that both,effects; will enlarge the cross-section of the fluid jet, and the rheological effect of non-Newtonian fluid dominates the process in general.

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.

Dislocation nucleation and emission from crack-tip

The problems of dislocation nucleation and emission from a crack tip are analysed based on Peierls model. The concept adopted here is essentially the same as that proposed by Rice. A slight modification is introduced here to identify the pure linear elastic response of material. A set of new governing equations is developed, which is different from that used by Beltz and Rice. The stress field and the dislocation density field can be expressed as the first and second Chebyshev polynomial series respectively. Then the opening and slip displacements can be expanded as the trigonometric series. The Newton-Raphson Method is used to solve a set of nonlinear algebraic equations. The new governing equations allow us to extend the analyses to the case of dislocation emission. The calculation results for pure shearing, pure tension and combined tension and shear loading are given in detail.

The effects of capillary force in micro or nano-indentation

Models describing wet adhesion between indenters and substrates joined by liquid bridges are investigated. The influences of indenter shapes and various parameters of structures on capillary force are focused. In the former, we consider several shapes, such as conical, spherical and truncated conical indenter with a spherical end. In the latter, the effects of the contact angle, the environmental humidity, the gap between the indenter and the substrate, etc. are included. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. Most interesting finding is that applying the present results to micro- and nano-indentation experiments shows the size effect in indentation hardness not produced but underestimated by the effects of capillary force.(4 refs)